BUSN 311 Type I Error Is Defined as Rejection of True Null Hypothesis

Description

You must respond to at least 2 other students outside your initial thread. Responses should be a minimum of 50 words and may include direct questions.

In your first peer response post, look at the hypothesis test results of one of your classmates and explain what a type 1 error would mean in a practical sense. Looking at your classmate’s outcome, is a type 1 error likely or not? What specific values indicated this?

In your second peer response post, using your classmate’s values, run another hypothesis test using this scenario: A town official claims that the average vehicle in their area Does Not sell for 80th percentile of your data set. Conduct a four-step hypothesis test including a sentence at the end justifying the support or lack of support for the claim and why you made that choice. Note: this test will be different than the initial post, starting with the hypothesis scenario. Use alpha = .05 to test your claim.

The reading below pertains to lesson for this forum.

Read Quantitative Information Analysis III Chapter 8 & 9

This week we will explore the following topics:

Hypothesis Testing (8.1, 8.2 and 9.1)
Outcomes, Errors and Distribution (8.3, 8.4, 8.5)
Rare Events, Sample and Test Examples (8.6, 8.7, 8.8)
Hypothesis Testing with Two Samples- Unknown Standard Deviations (9.2)
Hypothesis Testing with Two Samples, Known Standard Deviations (9.3)
Comparing Two Independent Population Proportions (9.4)
Matched or Paired Samples (9.5)

Forum Post 1:

Hello class,

For this prompt, 40th percentile of my data is $41,000. From doing

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some research on the differences between z- and t-tests, I would say that this would need to be a t-test because we know the sample and are trying to test a hypothesis instead of comparing a population. In this scenario, I ran an upper tailed test since there is a greater than sign because the problem asked for a “more than”.

Ho: ̅= 41,000
Ha: ̅> 41,000
T-Stat = 52,580 – 41,000 / 12,735.60 = 0.9093
P-value = 0.19344
0.19 > 0.05

Looking at step 4, since the p-value is greater than the alpha, this means we will not reject Ho. This means we will not reject the claim that the mean price for a car is $41,000. This proves the town official wrong because we could not accept Ha.

I thought this was kind of an interesting exercise and at times I got a little confused, but I’m open to feedback in case it looks like I did something wrong.

Forum Post 2:

Good evening class,

Happy Veterans Day to all the Veterans and family members in this class.

My data set is as follows,

Mean: 59,664

Standard Error: 6,597.19

40th Percentile: 56,967.40

Step 1:

HO: X = 56,976.40

HA: X > 56,976.40

Step 2:

T-stat: 0.4087497859

Step 3:

P-Value: 0.34613914

Step 4:

0.34 > 0.05

There are parts of the equation I do not have a lot of confidence with so please let me know if you see any errors. Attached is the data set I used for my calculations.

From my calculations, the 40th percentile of my data set is 56,967.40. I found that it is proven the town official’s claim is wrong. We will not accept the hypothesis and the we do not accept the Ha, we do accept the Ho.

Statistics has been one of the harder classes I have taken for myself, but I feel like this week’s lesson brought a lot of the concepts together for me. Good luck to everyone this week.

Read; George and Sophia are entrepreneurs who together own a limited liability company, SOPhiGEo, LLC.

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